For what values of x is the following inequation valid : 2x^2+ 14x + 24 > 0

We are given the following inequation to solve 2x^2+ 14x +
24 > 0

Now, 2x^2+ 14x + 24 >
0

=> 2x^2 + 6x + 8x +24
>0

=> 2x ( x +3) + 8 (x+3)
>0

=>
(x+4)(x+3)>0

Now as (x+4)(x+3) is greater than 0.
Either (x+4)and (x+3)can be greater than 0 or they can both be less than
0.

If they are greater than
0,

=> (x+4) > 0 and (x+3)
>0

=> x > -4 and x
>-3

=> x has to be greater than
-3

If both (x+4)and (x+3) are less than
0

=> (x+4) <0 and (x+3)
<0

=> x < -4 and x
<-3

=> x has to be less than
-4

Therefore x can be either greater than -3
or less than -4